Related papers: Greedy approximation in convex optimization

Dimensionality reduction on quadratic manifolds augments linear approximations with quadratic correction terms. Previous works rely on linear approximations given by projections onto the first few leading principal components of the…

The Column Subset Selection Problem provides a natural framework for unsupervised feature selection. Despite being a hard combinatorial optimization problem, there exist efficient algorithms that provide good approximations. The drawback of…

In this experimental study we consider Steiner tree approximations that guarantee a constant approximation of ratio smaller than $2$. The considered greedy algorithms and approaches based on linear programming involve the incorporation of…

We study the problem that requires a team of robots to perform joint localization and target tracking task while ensuring team connectivity and collision avoidance. The problem can be formalized as a nonlinear, non-convex optimization…

We give an efficient algorithm for finding sparse approximate solutions to linear systems of equations with nonnegative coefficients. Unlike most known results for sparse recovery, we do not require {\em any} assumption on the matrix other…

We propose a general formulation of nonconvex and nonsmooth sparse optimization problems with convex set constraint, which can take into account most existing types of nonconvex sparsity-inducing terms, bringing strong applicability to a…

Identifying cause-effect relations among variables is a key step in the decision-making process. While causal inference requires randomized experiments, researchers and policymakers are increasingly using observational studies to test…

A flaw in the greedy approximation algorithm proposed by Zhang et al. for minimum connected set cover problem is corrected, and a stronger result on the approximation ratio of the modified greedy algorithm is established. The results are…

In this paper, we develop a randomized algorithm and theory for learning a sparse model from large-scale and high-dimensional data, which is usually formulated as an empirical risk minimization problem with a sparsity-inducing regularizer.…

Kernel methods are versatile tools for function approximation and surrogate modeling. In particular, greedy techniques offer computational efficiency and reliability through inherent sparsity and provable convergence. Inspired by the…

We consider concave minimization problems over non-convex sets.Optimization problems with this structure arise in sparse principal component analysis. We analyze both a gradient projection algorithm and an approximate Newton algorithm where…

Polynomial optimization problems are infinite-dimensional, nonconvex, NP-hard, and are often handled in practice with the moment-sums of squares hierarchy of semidefinite programming bounds. We consider problems where the objective function…

In dictionary selection, several atoms are selected from finite candidates that successfully approximate given data points in the sparse representation. We propose a novel efficient greedy algorithm for dictionary selection. Not only does…

Optimization problems are ubiquitous in our societies and are present in almost every segment of the economy. Most of these optimization problems are NP-hard and computationally demanding, often requiring approximate solutions for…

Recently, neural networks have been widely applied for solving partial differential equations (PDEs). Although such methods have been proven remarkably successful on practical engineering problems, they have not been shown, theoretically or…

We consider learning a convex combination of basis models, and present some new theoretical and empirical results that demonstrate the effectiveness of a greedy approach. Theoretically, we first consider whether we can use linear, instead…

The paper deals with the problem of finding sparse solutions to systems of polynomial equations possibly perturbed by noise. In particular, we show how these solutions can be recovered from group-sparse solutions of a derived system of…

Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…

We address the problems of minimizing and of maximizing the spectral radius overa compact family of non-negative matrices. Those problems being hard in generalcan be efficiently solved for some special families. We consider the so-called…

We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…